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Burr distribution is one of the most important types of distribution in Burr system and has gained special attention. It has an important role in various disciplines, such as reliability analysis, life testing, survival analysis, actuarial science, economic, forestry, hydrology, and meteorology. Thus, parameter estimation for Burr distribution becomes an important thing to do. Frequentist approach using the maximum likelihood method is the most commonly used way to estimate the parameters of a distribution. In this paper we considered using the Bayesian method to estimate the shape parameter k of Burr distribution using gamma prior which is a conjugate prior. Bayes estimator for the shape parameter k is obtained under the squared-error loss function (SELF) which is one of the symmetric loss function and the precautionary loss function (PLF) which is one of the asymmetric loss function. Through a simulation study, the comparison was made on the performance of Bayes estimators for the shape parameter k under these two loss functions with respect to the mean-squared error (MSE) and the posterior risk of each estimator. The results of comparison show that with respect to the MSE, Bayes estimator for the shape parameter k under the SELF gives better results. However, with respect to the posterior risk, Bayes estimator for the shape parameter k under the SELF gives better results if the true value of the shape parameter k is less than 1, while Bayes estimator under the PLF gives better results if the true value of the shape parameter k is more than or equal to 1. Based on the results of this simulation study, we can conclude that estimation for the shape parameter k of Burr distribution using Bayesian method under the squared-error loss function as a symmetric loss function is found to be superior compared to the precautionary loss function as a asymmetric loss function with respect to the mean-squared error, but estimation under the squared-error loss function is found to be superior in turn with the precautionary loss function with respect to the posterior risk.

Bayesian method; Burr distribution; precautionary loss function; squared-error loss function